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The crystalline form of carbon has a definite structural arrangement, but non-crystalline isn't. Atoms in the non-crystalline form are arranged randomly without any fixed pattern or shape. This form is also called an amorphous form of carbon.
Crystalline form eg., Diamond, Graphite, Fullerene, Buckyballs, Carbon Nanotubes, etc.
Non-crystalline eg., Coal, Coke, etc.